1.  The Problem of Exchange

2.  Given an economy where individuals are allocated a certain amount of goods, we will o Investigate barter exchange o define equilibrium trade o Investigate the emergence of competitive markets

3.  Primitive, two-person economy o Geoffrey, Elizabeth o Harvest & gather fruit Apples, raspberries o Voluntary trade – beneficial o Options Consume all Trade some 3

4.  Edgeworth box o Graphical device to analyze the process of trade o Its size equals the total amount of goods o A point in the box represents a possible/ feasible allocation of goods 4

5.  No-trade allocation o Feasible allocation o No trade o Individuals consume their own harvest 5

6. 6 Dimensions of the Edgeworth box represent total amount of each good. There are 10 apples and 8 raspberries Raspberries 0 8 Apples 10

7. 7 Raspberries to Geoffrey 0 28 Apples to Geoffrey 8 10 f Apples to Elizabeth 2 Raspberries to Elizabeth 06 Geoffrey Elizabeth I 1g I 1e

8.  Equilibrium allocation o Once reached o No incentive to further trade  Block o Prevent a trade o Coalition – each gets more  Individually rational trade o Higher utility - than no trade 8

9. 9 The shaded, lens-shaped area represents the set of allocations that do not lower either agent’s utility relative to the no-trade allocation at point f. Raspberries to Geoffrey 0 248 Apples to Geoffrey 6 8 10 f Apples to Elizabeth 2 4 Raspberries to Elizabeth 064 h g j i I 1g I 1e I 2e I 3e I 3g I 2g

10.  Pareto-optimal (efficient) allocation o Allocation of goods across people o No other allocation can make one person better off without making the other worse off.  Not efficient allocation o Indifference curves cross  Efficient allocation o Indifference curves - tangent 10

11.  Efficient allocation o Tangency point - indifference curves o Marginal rates of substitution - same  Contract curve o Curve in Edgeworth box o All efficient trades 11

12. OGOG OEOE 12 The contract curve is a locus of all efficient trades, i.e., of all tangency points Apples to Elizabeth Raspberries to Elizabeth Apples to Geoffrey Raspberries to Geoffrey l k

13.  Contract curve o Set of efficient / Pareto optimal trades o No more voluntary trade will take place. 13

14. OGOG OEOE 14 The shaded, lens-shaped area represents the set of allocations that do not lower either agent’s utility relative to the no-trade allocation at point f. f C A Apples to Elizabeth Raspberries to Elizabeth Apples to Geoffrey Raspberries to Geoffrey I 1g I 1e m l n k Blocked by Elizabeth Blocked by Geoffrey

15.  Core of economy o Set of equilibrium trades o Portion of contract curve Between no-trade indifference curves o Individually rational o Cannot be blocked 15

16.  Economy – grows through replication  As we add agents o Set of core allocation – diminish o Points on original core – eliminated 16

17. 17 G1 and G2 will negotiate with E2 a better deal: Each G offers 2.5 apples and gets in return 0.5 raspberries f C A Apples to Elizabeth Raspberries to Elizabeth Apples to Geoffrey Raspberries to Geoffrey m n z 3 5 5 1212 2 1212 37 82 2 6

18.  Economy – grows larger o Set of core allocations – one point  Competitive behavior o Price-taking behavior o Individuals take prices as given o Based on the value of their endowments decide how much of each good to buy  Competitive Equilibrium o Set of prices that clear markets (QD=QS of each good) o Determined by the endowment and individual preferences 18

19. 19 f C A Apples to Elizabeth Raspberries to Elizabeth Apples to Geoffrey Raspberries to Geoffrey e

20. 20 Point e f D C B A Apples to Elizabeth Raspberries to Elizabeth Apples to Geoffrey Raspberries to Geoffrey y z

21.  A Competitive Equilibrium is defined by a set of prices such that o For any good o Total Quantity demanded= Total Quantity Supplied o At those prices 21

22.  To solve: o Find the demand for each good by each individual Use the utility function Individual income evaluated at the competitive prices o Calculate market demand by adding up all individual demand o Total supply is total amount of good i. o Set total demand = total supply 22